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Simplifying 2w + -2 + 4(3w + 1) = -2(w + 8) Reorder the terms: 2w + -2 + 4(1 + 3w) = -2(w + 8) 2w + -2 + (1 * 4 + 3w * 4) = -2(w + 8) 2w + -2 + (4 + 12w) = -2(w + 8) Reorder the terms: -2 + 4 + 2w + 12w = -2(w + 8) Combine like terms: -2 + 4 = 2 2 + 2w + 12w = -2(w + 8) Combine like terms: 2w + 12w = 14w 2 + 14w = -2(w + 8) Reorder the terms: 2 + 14w = -2(8 + w) 2 + 14w = (8 * -2 + w * -2) 2 + 14w = (-16 + -2w) Solving 2 + 14w = -16 + -2w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2w' to each side of the equation. 2 + 14w + 2w = -16 + -2w + 2w Combine like terms: 14w + 2w = 16w 2 + 16w = -16 + -2w + 2w Combine like terms: -2w + 2w = 0 2 + 16w = -16 + 0 2 + 16w = -16 Add '-2' to each side of the equation. 2 + -2 + 16w = -16 + -2 Combine like terms: 2 + -2 = 0 0 + 16w = -16 + -2 16w = -16 + -2 Combine like terms: -16 + -2 = -18 16w = -18 Divide each side by '16'. w = -1.125 Simplifying w = -1.125
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